English
Hindi

Question

Download Solution PDF

A root x4 – 3x + 1 = 0 needs to be found using the Newton-Raphson method. If the initial guess x0 and 0, then the new estimate x1 after the first iteration is

This question was previously asked in
BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)
Download PDF Attempt in App
View all BPSC Assistant Professor Papers >
  1. -3
  3. 3

Answer (Detailed Solution Below)

Option 4 :

Detailed Solution

Download Solution PDF

Concept:

Newton-Raphson Method:

The iteration formula is given by

Where x0 is the initial value/root of the equation f(x) = 0

Calculation:

Given:

f(x) = x4 - 3x + 1, x0 = 0

f'(x) = 4x3 - 3

f(x0) = 0 - 0 + 1 = 1,

f'(x0) = 0 - 3 = -3

We know that

Download Solution PDF
Latest BPSC Assistant Professor Updates

Last updated on Jun 23, 2025

-> The Document Verification for BPSC Assistant Professor (Advt. No. 04/2025 to 28/2025) will be conducted between 7th July 2025 to 24th July 2025

-> The BPSC Assistant Professor Notification 2025 was released for 1711 vacancies under Speciality (Advt. No.04/2025 to 28/2025).

-> The recruitment is ongoing for 220 vacancies (Advt. No. 01/2024 to 17/2024).

-> The salary under BPSC Assistant Professor Recruitment is approximately Rs 15600-39100 as per Pay Matrix Level 11. 

-> The selection is based on the evaluation of academic qualifications &  work experience and interview.

-> Prepare for the exam using the BPSC Assistant Professor Previous Year Papers. For mock tests attempt the BPSC Assistant Professor Test Series.

Exams Tests Super Practice

More Numerical Solutions of Nonlinear Algebraic Equations Questions

Q1.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q2.The iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Q3.The iteration step in order to solve for the cube roots of a given number Nusing the Newton- Raphson’s method is
Q4.The real root of x3 + x2 + 3x + 4 = 0 correct to four decimal places, obtained using Newton Raphson method is
Q5.The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will be
Q6.To solve the equation 2 sin x = x by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be closest to
Q7.The Newton-Raphson method is said to have
Q8.If the equation sin (x) = x2 is solved by Newton Raphson’s method with the initial guess of x = 1, then the value of x after 2 iterations would be _______
Q9.During the determination of roots of equations x2 + 2xy = 6 and x2 - y2 = 3 using the Newton-Raphson method, the values of Jacobin matrix ‘D’ is found to be ______. If initial approximation is (1.414, 0.517).
Q10.To find the root of f(x) = 0 by using the bisection method, an iteration is begun with the lower and upper guesses of the root. If xlower and xupper are the roots, then at the end of the iteration, the absolute relative approximate error in the estimated value of the root would be

More Numerical Methods Questions

Q1.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q2.The rate of convergence of Newton Raphson method is :
Q3.If the value of the approximate solution of the initial value problem   \(\rm \left\{\begin{matrix}y'(x)=x(y(x)+1), &x\in R\\\ y(0)=β \end{matrix}\right.\) at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 
Q4.The iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Q5.In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to-
Q6.If \(\frac{dy}{dx}\) = x - y2 and y(0) = 1, then y(0.1) correct upto two decimal places (approx.) is:
Q7.In which of the following categories can we put Bisection method?
Q8.Which order of Polynomials can best be integrated using Trapezoidal Rules?
Q9.Consider the differential equation \(\rm \frac{dy}{dx}=4(x+2)-y \) For the initial condition y = 3 at x = 1, the value of 𝑦 at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is _________. (round off to one decimal place)
Q10.Consider the following recursive iteration scheme for different values of variable P with the initial guess x1 = 1. \(x_{n+1}=\frac{1}{2}\left(x_n+\frac{P}{x_n}\right)\), n = 1, 2, 3, 4, 5 For P = 2, x5 is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x5 is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x5 is ________. (round off to three decimal places)
Suggested Test Series
View All >
71st BPSC CCE (Preliminary) Test Series 2025
215 Total Tests with 1 Free Tests
Start Free Test
BPSC बिहार माध्यमिक TGT (9 to 10) शिक्षक भर्ती 4.0 Mock Test
577 Total Tests with   2 Free Tests
Start Free Test

UPPSC AE Important Links

VacancyEligibility CriteriaExam PatternSyllabusSalary & Job ProfileResult

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti bodhi teen patti apk teen patti master king teen patti master 2024